Non-invasive method and system for measuring myocardial ischemia, stenosis identification, localization and fractional flow reserve estimation

ABSTRACT

The present disclosure facilitates the evaluation of wide-band phase gradient information of the heart tissue to assess, e.g., the presence of heart ischemic heart disease. Notably, the present disclosure provides an improved and efficient method to identify and risk stratify coronary stenosis of the heart using a high resolution and wide-band cardiac gradient obtained from the patient. The patient data are derived from the cardiac gradient waveforms across one or more leads, in some embodiments, resulting in high-dimensional data and long cardiac gradient records that exhibit complex nonlinear variability. Space-time analysis, via numeric wavelet operators, is used to study the morphology of the cardiac gradient data as a phase space dataset by extracting dynamical and geometrical properties from the phase space dataset.

RELATED APPLICATIONS

This application claims priority to, and the benefit of, U.S.Provisional Application No. 62/354,673, filed Jun. 24, 2016, and U.S.Provisional Application No. 62/409,176, filed Oct. 17, 2016, each ofwhich is incorporated by reference herein in its entirety.

FIELD OF THE INVENTION

The present disclosure generally relates to non-invasive methods andsystems for characterizing cardiovascular circulation. Morespecifically, the present disclosure relates to non-invasive methodsthat utilize unfiltered wide-band cardiac phase gradient data togenerate residue subspace and noise subspace data, for example, to beused in the prediction and localization of coronary artery stenoses,localizing and/or estimating fractional flow reserve, and characterizingmyocardial ischemia.

BACKGROUND

Vascular diseases are often manifested by reduced blood flow due toatherosclerotic occlusion of vessels. For example, occlusion of thecoronary arteries supplying blood to the heart muscle is a major causeof heart disease. Invasive procedures for relieving arterial blockagesuch as bypass surgery and stent placement with a catheter rely onestimates of occlusion characteristics and blood flow through theoccluded artery. These estimates are based on measurements of occlusionsize and/or blood flow. Unfortunately, current methods of occlusion sizeand blood flow measurement require invasive procedures such as coronaryangiography, which requires cardiac catheterization. This procedureinvolves a long, thin, flexible catheter being placed into a bloodvessel in the arm, groin (upper thigh), or neck; the catheter is thenthreaded to the heart. Through the catheter, a physician can perform avisual evaluation of the inner diameter of a vessel with cineangiographyor fluoroscopy and/or use a small sensor on the tip of the wire(commonly a transducer) to measure parameters such as pressure,temperature, and flow to determine the severity of the lesion; andfractional flow reserve (FFR). These minimally invasive diagnostic testson the heart carry the risk of stroke, heart attack, injury to thecatheterized artery/heart, irregular heart rhythms, kidney damage,infection, and radiation exposure from X-rays. These procedures are timeconsuming, require expertise in the interpretation of the results andare expensive.

Stenosis geometry is also important in the therapeutic phase whenballoon angioplasty, stenting or drug delivery procedures aresubsequently performed. For example, precise stent placement is criticalfor reducing the risk of restenosis. Thus, decisions on whether or notto use any of the blockage relieving methods and which of the methodsshould be used are often based on partial information and do not takeinto account coronary collateralization. The ischemic stress ofteninduces the increase in collateral circulation in coronary small vesselwhich at times will compensate for distal vessel blockage. Further, theevaluation of therapeutic success is also problematic, where bothocclusion opening and stent position have to be evaluated. One class ofmethods, predominantly used today, require a lengthy procedure to findand determine severity, blockage to blood flow, of the lesion orlesions. Contemporary techniques evaluate the cardiac gradientphase-space changes and correlate the changes with cardiac computedtomography (CT), myocardial perfusion imaging, and cardiac angiography.The surface cardiac gradient contains detailed information on theelectrophysiology of the chambers recorded. Because surface cardiacgradient represents the summation of the individual action potentialsfrom each and every cardiac cell in syncytium, in theory, anyinformation that might be determined from measurement of theorchestrated cellular action potential should be available on a “global”level in the surface. Moreover, although information relating to theinfluence of myocardial tissue architecture on conduction properties isinherent in the surface cardiac gradient, the challenge is in thediscrimination of the pertinent information from these longquasi-periodic cardiac gradient signals while excluding noisecontamination. Still further, there is a distinct lack of non-invasivetools available to enhance identification of high-risk patients and thusto trial preventive strategies in a non-invasive manner.

SUMMARY

The present disclosure facilitates the evaluation of wide-band phasegradient information of heart tissue to assess the presence of heartischemic heart disease. Notably, the present disclosure provides animproved and efficient method to identify and risk-stratify coronarystenosis of the heart using a high resolution and wide-band cardiacgradient obtained from the patient or subject. The patient data arederived from the cardiac gradient waveforms across multiple leads, insome embodiments, resulting in high-dimensional data and long cardiacgradient records that exhibit complex nonlinear variability. Space-timeanalysis, via numeric wavelet operators, is used to study the morphologyof the cardiac gradient data as a phase space dataset by extractingdynamical and geometrical properties from the phase space dataset. Thenumeric wavelet operators facilitate real-time, or near real-timeprocessing of the collected wide-band cardiac gradient dataset togenerate a residue subspace dataset and a noise subspace dataset. Theresidue subspace dataset and noise subspace dataset, in someembodiments, are generated as multi-dimensional datasets (e.g.,three-dimensional) and are well-suited to image and graphics processing.The extracted morphology of the residue subspace dataset and noisesubspace dataset are fed, as parameters and variables, to a learningalgorithm to associate them with abnormalities of the heart understudy.

As such, the present disclosure provides for a non-invasive system andmethod whereby cardiac gradient measurements can be taken andtransformed to locate and visualize, via rendered images, architecturalfeatures of the myocardium and to characterize abnormalities in theheart and the cardiovascular function. Furthermore, the presentdisclosure provides a system and method to visualize (e.g., an inversecardiac gradient problem) architectural features of the heart and thelocation of abnormally conducting/functioning cardiac tissue.Furthermore, the present disclosure provides a system and method tooutput, as parameters, to therapy, a treatment device, or a diagnosticdevice, architectural features of the heart and the location ofabnormally conducting/functioning cardiac tissue.

In an aspect, a method or methods are disclosed of non-invasivelyidentifying and/or measuring myocardial ischemia, identifying one ormore stenoses, and/or localizing and/or estimating fractional flowreserve in a mammalian subject or patient. The method(s) include(s)obtaining a plurality of wide-band gradient signals simultaneously fromthe subject via at least one of electrode (e.g. one or more surfaceelectrodes, non-contact electrodes or other types of biopotentialsensing apparatus) and determining, via one or more processors, one ormore coronary physiological parameters of the subject selected from thegroup consisting of a fractional flow reserve estimation, a stenosisvalue, and a myocardial ischemia estimation (e.g., and/or other arterialflow characteristics), based on a residue subspace dataset and a noisesubspace dataset derived from data associated with the plurality ofwide-band gradient signals.

In some embodiments, the residue subspace dataset is determined bygenerating a first wavelet signal dataset by performing a first waveletoperation (via, e.g., a first phase linear wavelet operator) on dataderived from the plurality of wide-band gradient signals; generating asecond wavelet signal dataset by performing a second wavelet operation(via, e.g., a second phase linear wavelet operator) on the first waveletsignal data; and subtracting values of the first wavelet signal datasetfrom values of the second wavelet signal dataset to generate the residuesubspace dataset, wherein the residue subspace dataset comprises athree-dimensional phase space dataset in a space-time domain.

In some embodiments, the method or methods further include(s) extractinga first set of morphologic features of the three-dimensional phase spacedataset, wherein the first set of extracted morphologic features includeparameters selected from the group consisting of a three-dimensional(3D) volume value, a void volume value, a surface area value, aprincipal curvature direction value, and a Betti number value.

In some embodiments, the first set of extracted morphologic features isextracted using an alpha-hull operator.

In some embodiments, the method or methods further include(s) dividingthe three-dimensional phase space dataset into a plurality of segments,each comprising non-overlapping portions of the three-dimensional phasespace data set and extracting a second set of morphologic features ofeach of the plurality of segments, wherein the second set of extractedmorphologic features includes parameters selected from the groupconsisting of a 3D volume value, a void volume value, a surface areavalue, a principal curvature direction value, and a Betti number value.

In some embodiments, the second set of extracted morphologic features isextracted using an alpha-hull operator.

In some embodiments, the plurality of segments comprises a number ofsegments selected from the group consisting of 3, 4, 5, 6, 7, 8, 9, 10,11, 12, 13, 14, 15, 16, 17, 18, 19, and 20.

In some embodiments, the noise subspace dataset is determined bygenerating a first wavelet signal dataset by performing a first waveletoperation (e.g., a first phase linear wavelet operator) on data derivedfrom the plurality of wide-band gradient signals and generating a secondwavelet signal dataset by performing a second wavelet operation (e.g., asecond phase linear wavelet operator) on the first wavelet signal data,the second wavelet signal data comprising the noise subspace dataset,wherein the noise subspace dataset comprises a 3D phase space dataset ina space-time domain.

In some embodiments, the method or methods further include(s) extractinga set of morphologic features of the 3D phase space data set, whereinthe set of extracted morphologic features includes parameters selectedfrom the group consisting of a 3D volume value, a void volume value, asurface area value, a principal curvature direction value, and a Bettinumber value.

In some embodiments, the set of extracted morphologic features isextracted using an alpha-hull operator.

In some embodiments, the method or methods further include(s) dividingthe three-dimensional phase space data set into a plurality of segments,each comprising non-overlapping portion of the three-dimensional phasespace dataset and extracting a second set of morphologic features ofeach of the second plurality of segments, wherein the second set ofextracted morphologic features includes parameters selected from thegroup consisting of a 3D volume value, a void volume value, a surfacearea value, a principal curvature direction value, and a Betti numbervalue.

In some embodiments, the second set of extracted morphologic features isextracted using an alpha-hull operator.

In some embodiments, the second of segments comprises a number ofsegments selected from the group consisting of 3, 4, 5, 6, 7, 8, 9, 10,11, 12, 13, 14, 15, 16, 17, 18, 19, and 20.

In some embodiments, the residue subspace dataset is associated with afirst shape of a first noise geometry and the noise subspace dataset isassociated with a second shape of a second noise geometry correspondingto stochastic noise.

In some embodiments, the plurality of wide-band gradient signals aresimultaneously obtained having a lag or skew of less than about10-femtoseconds between each of the signals.

In some embodiments, each of the plurality of wide-band gradient signalsis unfiltered prior to, and during, the processing, to generate theresidue subspace dataset and the noise subspace dataset.

In some embodiments, each of the plurality of wide-band gradient signalscomprises cardiac data in a frequency domain having frequency componentsgreater than about 1 kHz.

In some embodiments, each of the plurality of wide-band gradient signalscomprises cardiac frequency information at a frequency selected from thegroup consisting of about 1 kHz, about 2 kHz, about 3 kHz, about 4 kHz,about 5 kHz, about 6 kHz, about 7 kHz, about 8 kHz, about 9 kHz, andabout 10 kHz.

In some embodiments, each of the plurality of wide-band gradient signalscomprises cardiac frequency information at a frequency between about 0Hz and about 50 kHz.

In some embodiments, each of the plurality of wide-band gradient signalscomprises cardiac frequency information at a frequency between about 0Hz and about 500 kHz.

In some embodiments, the method or methods further include(s)associating, via a first machine learning operation (e.g., neural nets,formula learning, etc.), the extracted first set of morphologic featuresto a plurality of candidate models associated with estimation of thefractional flow reserve estimation, the stenosis value, and themyocardial ischemia estimation; and selecting a candidate model of theplurality of candidate models to determine an output of each of theestimation of the fractional flow reserve estimation, the stenosisvalue, and the myocardial ischemia estimation.

In some embodiments, the method or methods further include(s)visualizing the determined one or more coronary physiologicalparameters.

In some embodiments, the fractional flow reserve estimation, thestenosis value, and the myocardial ischemia estimation are presented atone or more corresponding coronary regions on an image of a heart (e.g.,via a standardized 17-segment model of the heart).

In some embodiments, the method or methods further include(s)outputting, to a surgical device or a diagnostic device, the determinedone or more coronary physiological parameters.

In some embodiments, one of more of the at least one electrode areselected from the group consisting of surface electrodes, intracardiacelectrodes, and non-contact electrodes.

In some embodiments, the methods include(s) identifying one or moresignificant artery stenoses, the identification having an AUC-ROC score(“area-under-the-curve” and “receiver operating characteristic” score)greater than about 0.7 in a verification phase.

In another aspect, a system is disclosed, e.g., of non-invasivelyidentifying and/or measuring myocardial ischemia, identifying one ormore stenoses, and/or localizing and/or estimating fractional flowreserve, e.g., via a wide-band biopotential measuring apparatus. Thesystem includes a processor and a memory having instructions storedthereon, wherein execution of the instructions causes the processor toobtain a plurality of wide-band gradient signals simultaneously from oneor more electrodes (e.g., surface electrodes, non-contact electrodes orother types of biopotential sensing apparatus) and determine one or morecoronary physiological parameters selected from the group consisting ofa fractional flow reserve estimation, a stenosis value, and a myocardialischemia estimation, based on a residue subspace dataset and a noisesubspace dataset derived from data associated with the plurality ofwide-band gradient signals.

In some embodiments, execution of the instructions further causes theprocessor to cause visualization of the determined coronaryphysiological parameter to be presented on a display.

In some embodiments, the execution of the instructions further causesthe processor to output, to a therapy device, the determined one or morecoronary physiological parameters.

In another aspect, a computer readable medium is disclosed havinginstructions stored thereon, wherein execution of the instructionscauses a processor to determine one or more coronary physiologicalparameters selected from the group consisting of a fractional flowreserve estimation, a stenosis value and a myocardial ischemiaestimation, based on a residue subspace dataset and a noise subspacedataset derived from data associated with the plurality of wide-bandgradient signals simultaneously obtained from at least one surfaceelectrode.

In some embodiments, execution of the instructions further causes theprocessor to cause visualization of the determined coronaryphysiological parameter to be presented on a display.

In some embodiments, execution of the instructions causes the processorto output, to a therapy device, the determined one or more coronaryphysiological parameters.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

The components in the drawings are not necessarily to scale relative toeach other and like reference numerals designate corresponding partsthroughout the several views:

FIG. 1 is a diagram of a system for non-invasively determining arterialflow characteristics (e.g., presence of myocardial ischemia, stenosisidentification, localization, and fractional flow reserve estimation) inthe heart using wide-band cardiac gradient data, in accordance with anillustrative embodiment.

FIG. 2 is a diagram of an example wide-band cardiac gradient signalshown as a time series data, in accordance with an illustrativeembodiment.

FIG. 3 is a diagram of an example wide-band cardiac gradient signalshown in the frequency domain, in accordance with an illustrativeembodiment.

FIG. 4 is a time-series plot of an example wide-band cardiac gradientsignal associated with a single surface electrode, in accordance with anillustrative embodiment.

FIG. 5 is a frequency plot of an example wide-band cardiac gradientsignal associated with three surface electrodes, in accordance with anillustrative embodiment.

FIG. 6 is a frequency plot of an example ultra-wide-band cardiacgradient signal associated with three surface electrodes, in accordancewith an illustrative embodiment.

FIG. 7 is a diagram of a method of processing wide-band cardiac gradientsignal to non-invasively identify and/or estimate a degree of myocardialischemia, stenosis identification, and/or localization and fractionalflow reserve estimation, in accordance with an illustrative embodiment.

FIG. 8 is a diagram of a method of performing feature topology analysis,e.g., of a multi-dimensional residue subspace dataset, amulti-dimensional noise subspace dataset, and a multi-dimensionalwavelet cleansed dataset, in accordance with an illustrative embodiment.

FIG. 9 is a diagram of a method of performing machine learning analysisto create and select non-linear models to identify and/or estimate adegree of myocardial ischemia, stenosis identification, and/orlocalization and fractional flow reserve estimation, as described inrelation to FIG. 8, in accordance with an illustrative embodiment.

FIGS. 10A and 10B are diagrams of an example wavelet transformation usedto generate the multi-dimensional wavelet cleansed dataset, inaccordance with an illustrative embodiment.

FIG. 11 is a diagram of an example time series dataset of a waveletcleansed dataset, in accordance with an illustrative embodiment.

FIG. 12 is a diagram of an example wavelet-based operation to generatethe multi-dimensional residue subspace dataset, in accordance with anillustrative embodiment.

FIGS. 13A and 13B are diagrams of an example wavelet transformation usedto generate the multi-dimensional wavelet cleansed dataset, inaccordance with an illustrative embodiment.

FIG. 14 is a depiction of an example multi-dimensional residue subspacedataset, in accordance with an illustrative embodiment.

FIG. 15 is a depiction of an example multi-dimensional noise subspacedataset, in accordance with an illustrative embodiment.

FIGS. 16 and 17 are each a depiction of an example multi-dimensionalresidue subspace dataset, in accordance with an illustrative embodiment.FIG. 16 shows an example multi-dimensional residue subspace dataset of asubject without ischemia. FIG. 17 shows an example multi-dimensionalresidue subspace dataset of a subject with ischemia.

FIGS. 18 and 19 are each a depiction of an example multi-dimensionalnoise subspace dataset, in accordance with an illustrative embodiment.FIG. 18 shows an example multi-dimensional noise subspace dataset of asubject without ischemia. FIG. 19 shows an example multi-dimensionalnoise subspace dataset of a subject with ischemia.

FIG. 20 is a diagram of a method of visualizing the determined arterialflow characteristics in the heart, in accordance with an illustrativeembodiment.

FIGS. 21 and 22 are diagrams showing results of a study conducted usingthe analysis of FIG. 1, in accordance with an illustrative embodiment.

DETAILED DESCRIPTION

The components in the drawings are not necessarily to scale relative toeach other and like reference numerals designate corresponding partsthroughout the several views.

FIG. 1 is a diagram of a system for non-invasively determining arterialflow characteristics in the heart using wide-band cardiac gradient data,in accordance with an illustrative embodiment. As shown in FIG. 1, thesystem 100 includes a wide-band biopotential measuring equipment 102 andan analysis subsystem 104. The wide-band biopotential measuringequipment 102 collects wide-band biopotential signals 112 (shown as 112a . . . n) (also referred to herein as wide-band cardiac gradient signaldata 112) from a subject or patient 110, via at least one electrode 106(shown as surface electrodes 106 a, 106 b, . . . , 106 n), andcorresponding common-mode reference lead 108, all of which are in thesystem of FIG. 1 are attached to the surface of the mammalian subject orpatient 110 (e.g., the skin of an animal or a person). The wide-bandbiopotential measuring equipment 102 may be any device configured tocapture unfiltered electrophysiological signals such that the spectralcomponent(s) of the signals are not altered. That is, all of thecaptured signal, if not a significant portion of the captured signal,includes components conventionally perceived or treated as being noise,e.g., those in the frequency range of greater than about 1 kHz. To thisend, the wide-band biopotential measuring equipment 102 captures,converts, and analyzes the collected wide-band biopotential signals 112without any filtering (via hardware circuitry, or digital signalprocessing) that affects phase linearity of the signal of the wide-bandbiopotential signals 112. That is, only phase deterministic operations,numeric or analytical, are performed in the phase space transformationand analysis. Phase distortions are non-deterministic distortions thatcause shifts in the frequency component of a signal.

An example wide-band biopotential measuring equipment 102 is describedin U.S. patent application Ser. No. 15/248,838, published asUS2017/0119272, titled “Method and Apparatus for Wide-Band GradientSignal Acquisition,” which is incorporated by reference herein in itsentirety. In some embodiments, the wide-band biopotential measuringequipment 102 is configured to record unfiltered physiologic signals ata rate of about 8 kHz at a number of observation points on the patientor subject (in a resting position) for 210 seconds. The resultant signalrecording is then securely transmitted to a cloud-based repositorywhereupon it is automatically queued for processing. In someembodiments, the resultant signal recording is securely transmitted to acloud-based repository whereupon it is automatically queued forprocessing. The processing pipeline derives the phase energy of thethoracic system by taking the multi-dimensional (spatial temporal)transformation of the signals and subsequently reconstructs this into aphase space model of the patient's heart.

The inventors have discovered that wide-band biopotential signals,having energy and frequency components beyond those of conventionalelectrocardiography (ECG) and traditionally perceived or treated asrandom noise, includes measurable data of the heart physiology that canbe discriminated by genetic algorithms (and other machine learningalgorithms) to assess regional flow characteristics of the heart,including for example an estimated value for stenosis and theidentification of ischemia and a fractional flow reserve (FFR) ofspecific arteries and branches thereof. Noise removal (e.g., by applyingcleaning techniques to the data resulting in the same amount of data asprior to noise removal) is a fundamental step in signal processing.However, the exemplified method and system process the entire obtainedbiopotential signals without any noise removal operations. What hasheretofore been perceived and/or classified as unwanted noise in thewide-band data is, in many cases, the signal of interest. Examples ofnoise removal that is not performed include, but are not limited to,analog-based low-pass filters, band-pass filters, high-pass filters aswell as digital-based filters such as FIR filters, Butterworth filters,Chebyshev filters and median filters (among others) that are configuredto change the phase linearity of the processed signals. It is noted thatanalog-based low-pass filters, band-pass filters, high-pass filters aswell as digital-based filters, that are configured to be phase linear,may be used. In some embodiments, the signal may be processed via phaselinear operations to allow for analysis of specific aspects of thehigh-frequency wide-band data.

As described in U.S. patent application Ser. No. 15/248,838, in someembodiments, the wide-band biopotential measuring equipment 102 isconfigured to capture one or more biosignals, such as biopotentialsignals, in microvolt or sub-microvolt resolutions—resolutions that areat, or significantly below, the noise-floor of conventionalelectrocardiographic and biosignal acquisition instruments. In someembodiments, the wide-band biopotential measuring equipment 102 isconfigured to acquire and record wide-band phase gradient signals (e.g.,wide-band cardiac phase gradient signals, wide-band cerebral phasegradient signals) that are simultaneously sampled, in some embodiments,having a temporal skew or “lag” of less than about 1 μs, and in otherembodiments, having a temporal skew or lag of not more than about 10femtoseconds. Notably, the exemplified system minimizes non-lineardistortions (e.g., those that can be introduced via certain filters) inthe acquired wide-band phase gradient signal so as to not affect theinformation therein.

Referring still to FIG. 1, the analysis system 104 is configured togenerate a phase space map to be used in subsequent phase space analysis118 later described herein. The output of the phase space analysis isthen evaluated using machine learning analysis 120 to assess parameters122 associated with a presence of a disease or physiologicalcharacteristic such as regional arterial flow characteristics. In someembodiments, the machine learning analysis 120 may use a library 124 ofquantified FFR, stenosis, and ischemia data in the assessment of theobtained wide-band cardiac gradient signal data 112. The output 122 of aprocessor performing the analysis 104 is then transmitted to a graphicaluser interface, such as, e.g., a touchscreen or other monitor, forvisualization. The graphical user interface, in some embodiments, isincluded in a display unit configured to display parameters 122. In someembodiments, the graphical user interface displays intermediateparameters such as a 3D phase space plot representation of thebiopotential signal data and virtual biopotential signal data. In otherembodiments, the output of the processor is then transmitted to one ormore non-graphical user interfaces (e.g., printout, command-line ortext-only user interface), directly to a database or memory device for,e.g., later retrieval and/or additional analysis, or combinationsthereof.

As used herein, the term “processor” refers to a physical hardwaredevice that executes encoded instructions for performing functions oninputs and creating outputs. The processor may include one or moreprocessors, each configured to execute instructions and process data toperform one or more functions associated with a computer for indexingimages. The processor may be communicatively coupled to RAM, ROM,storage, database, I/O devices, and interface. The processor may beconfigured to execute sequences of computer program instructions toperform various processes.

Example Wide-Band Cardiac Gradient Signal

FIG. 2 (reproduced in FIG. 1) is a diagram of an example wide-bandcardiac gradient signal 112 shown as time series data, in accordancewith an embodiment. FIG. 3 (reproduced also in FIG. 1) is a diagram ofthe example wide-band cardiac gradient signal 112 of FIG. 2 shown in thefrequency domain, in accordance with an embodiment. As shown in FIG. 3,the wide-band cardiac gradient signal 112 has a frequency componentgreater than 1 kHz, which is significantly higher than conventionalelectrocardiogram measurements. In some embodiments, the wide-bandcardiac gradient signal 112 has a frequency component up to about 4 kHz(e.g., about 0 Hz to about 4 kHz). In some embodiments, the wide-bandcardiac gradient signal 112 has a frequency component up to about 5 kHz(e.g., about 0 Hz to about 5 kHz). In some embodiments, the wide-bandcardiac gradient signal 112 has a frequency component up to about 6 kHz(e.g., about 0 Hz to about 6 kHz). In some embodiments, the wide-bandcardiac gradient signal 112 has a frequency component up to about 7 kHz(e.g., about 0 Hz to about 7 kHz). In some embodiments, the wide-bandcardiac gradient signal 112 has a frequency component up to about 8 kHz(e.g., about 0 Hz to about 8 kHz). In some embodiments, the wide-bandcardiac gradient signal 112 has a frequency component up to about 9 kHz(e.g., about 0 Hz to about 9 kHz). In some embodiments, the wide-bandcardiac gradient signal 112 has a frequency component up to about 10 kHz(e.g., about 0 Hz to about 10 kHz). In some embodiments the wide-bandcardiac gradient signal 112 has a frequency component up to 50 kHz(e.g., about 0 Hz to about 50 kHz).

FIG. 4 is a time-series plot of an example wide-band cardiac gradientsignal 112 associated with a single surface electrode, in accordancewith an embodiment. The plot shows the signal in mV over time (inseconds)

FIG. 5 is a frequency plot of an example wide-band cardiac gradientsignal 112 associated with three surface electrodes, in accordance withan embodiment. As shown, FIG. 5 includes frequency components of thewide-band cardiac gradient signal 112 up to 4 kHz. As further shown, thepresented wide-band cardiac gradient signal 112 has power, in thefrequency domain, between −20 dB and 20 dB at frequencies greater than 1kHz. This portion 502 of the wide-band cardiac gradient signal 112includes topologic and functional information about the cardiac tissueand its underlying structure that can be used to determine regional flowcharacteristics such as estimation of regional FFR, estimation of regionstenosis, and identification and/or estimation of a degree of regionalischemia.

Wide-band cardiac gradient signals (e.g., having frequencies betweenabout 1 kHz and about 10 kHz) facilitate phase space analysis onunevenly sampled data. In some embodiments, the wide-band cardiacgradient signals have higher sampling rates during intervals of interestand lower sampling rates during other intervals to facilitateminimization of the resulting data set size. This varying sampling ratemay be used in application where data storage is limited. Manynon-linear functions (e.g., such as those used in phase space analysis)operate more effectively at identifying amplitudes with points that areunevenly spaced in the time domain. The much higher sampling rate ascompared to those of the highest frequencies of interest (e.g., 10 timesgreater than those of the highest frequencies of interest) facilitates acorrectly characterized shape of the signal system. This is similar toLorenz systems, where very high frequencies are beneficial to correctlymodel the shape of the system in phase space. Example of the Lorenzsystem is described in Lorenz, Edward Norton, “Deterministicnon-periodic flow”, Journal of the Atmospheric Sciences 20 (2), pages130-141 (1963), the entirety of which is hereby incorporated byreference.

Example Ultra-Wide-Band Cardiac Gradient Signal

In some embodiments, the exemplified method and system are used toclassify ultra-wide-band cardiac gradient signals having negativespectral energy signatures as high as about 500 kHz (e.g., havingfrequencies between about 1 kHz and about 500 kHz).

FIG. 6 is a frequency plot of an example ultra-wide-band cardiacgradient signal, in accordance with an illustrative embodiment. Asshown, FIG. 6 is sampled at a frequency of about 200 kHz and includesfrequency components of an ultra-wide-band cardiac gradient signal up toabout 100 kHz (according to the Nyquist sampling theorem). Notably, asshown, the presented ultra-wide-band cardiac gradient signal includesnegative spectral energy signatures in frequencies greater than about70-80 kHz (shown as frequencies 602); the negative spectral energysignatures, in the frequency domain, having energy between about 40 dBand about 50 dB. The data suggest that low-energy signatures inultra-wide-band electrocardiograms may have information that could beused to image morphologies or functions of the body and/or fordiagnostics.

Example Processing of Wide-Band Biopotential Signal Data

FIG. 7 is a diagram of a method 700 of processing the wide-bandbiopotential signal data 112 (and ultra-wide-band biopotential signaldata), in accordance with an illustrative embodiment. As shown in FIG.7, the method 700 includes collecting the wide-band gradient cardiacsignal data 112 (shown as “Wide-band gradient signals Unfiltered RAW ADCdata” 112) and pre-processing 702 the wide-band gradient cardiac signaldata to generate a phase space dataset (shown as “residue subspace”dataset 704 and “noise subspace” dataset 706) in phase space analysis,whereby features of the phase space dataset (704, 704) are extracted(operations 708) and evaluated in nested non-linear functions 710 togenerate stenosis and FFR estimation values 122.

The wide-band gradient cardiac signal data 112 may be collected from oneor more electrodes (e.g., surface electrodes, non-contact electrodes).In some embodiments, the wide-band gradient cardiac signal data 112 aresimultaneously collected from between 1 and about 20 or more electrodes(e.g., 1 electrode, 2 electrodes, 3 electrodes, 4 electrodes, 5electrodes, 6 electrodes, 7 electrodes, 8 electrodes, 9 electrodes, 10electrodes, 11 electrodes, 12 electrodes, 13 electrodes, 14 electrodes,15 electrodes, 16 electrodes, 17 electrodes, 18 electrodes, 19electrodes, and 20 or more electrodes). In some embodiments, thesampling of these electrodes may have a less than a 10-femtosecond skewor “lag”. In other embodiments, the sampling of these electrodes mayhave a less than a 100-femtosecond skew or lag. In other embodiments,the sampling of these electrodes may have a less than a few picosecondskew or lag. In some embodiments, the wide-band cardiac gradient signal112 has a frequency component up to about 10 kHz (e.g., about 0 Hz toabout 4 kHz; about 0 Hz to about 5 kHz; about 0 Hz to about 6 kHz; about0 Hz to about 7 kHz; about 0 Hz to about 8 kHz; about 0 Hz to about 9kHz; or about 0 Hz to about 10 kHz). In some embodiments, the wide-bandcardiac gradient signal 112 has a frequency component up to about 50 kHz(e.g., about 0 Hz to about 50 kHz). In some embodiments, the wide-bandgradient cardiac signal data 112 has a voltage resolution of about ½ μVsensitivity. In other embodiments, the wide-band gradient cardiac signaldata 112 has a voltage resolution greater than about ½ μV sensitivity(e.g., about 1 μV, about 10 μV, about 100 μV, or about 1 mV). In someembodiments, the resolution of the signal data is about 24 bits. In someembodiments, the effective resolution is 20 bits, 21 bits, 22 bits, or23 or more bits. In some embodiments, the effective resolution is lessthan 20 bits (e.g., 18 bits or 14 bits or fewer).

In some embodiments, the phase space plot analysis uses geometricalcontrast that arises from the interference in the phase plane of thedepolarization wave with any other orthogonal leads. The presence ofnoiseless subspaces allows the recording of the phase of these waves. Ingeneral, the amplitude resulting from this interference can be measured;however, the phase of these orthogonal leads still carries theinformation about the structure and generates geometrical contrast inthe image. The phase space plot analysis takes advantage of the factthat different bioelectric structures within, e.g., the heart and itsvarious types of tissue have different impedances, and so spectral andnon-spectral conduction delays and bends the trajectory of phase spaceorbit through the heart by different amounts. These small changes intrajectory can be normalized and quantified beat-to-beat and correctedfor abnormal or poor lead placement and the normalized phase spaceintegrals can be visualized on, or mapped to, a geometric mesh using agenetic algorithm to map 17 myocardial segments in the ventricle tovarious tomographic imaging modalities of the heart from retrospectivedata.

Referring still to FIG. 7, three separate phase space analyses areperformed to generate sets of metrics and variables (shown as 712 a, 712b, and 712 c) to be used in the non-linear functions 710 to generateregional FFR estimation values, regional stenosis values, and regionalischemia values 122. Table 1 is an example output matrix 122.

TABLE 1 Segment Vessel FFR Stenosis Ischemia 1 Left Main Artery (LMA)0.90 0.50 0.20 2 Proximal Left Circumflex Artery 0.85 0.60 0.30 (ProxLCX) 3 Mid-Left Circumflex Artery 0.93 0.35 0.15 (Mid LCX) 4 Distal LeftCircumflex Artery 1.00 0.00 0.00 (Dist LCX) 5 Left PosteriorAtrioventricular 1.00 0.00 0.00 (LPAV) 6 First Obtuse Marginal (OM1)0.60 0.95 0.72 7 Second Obtuse Marginal (OM2) 1.00 0.00 0.00 8 ThirdObtuse Marginal (OM3) 1.00 0.00 0.00 9 Proximal Left Anterior Descending1.00 0.00 0.00 Artery (Prox LAD) 10 Mid Left Anterior Descending Artery1.00 0.00 0.00 (Mid LAD) 11 Distal Left Anterior Descending 0.70 0.800.63 Artery (Dist LAD) 12 LAD D1 0.00 0.00 0.75 13 LAD D2 0.00 0.00 0.0014 Proximal Right Coronary Artery 0.00 0.00 0.00 (Prox RCA) 15 Mid RightCoronary Artery 0.00 0.00 0.00 (Mid RCA) 16 Distal Right Coronary Artery0.00 0.00 0.18 (Dist RCA) 17 Acute Marginal Brach Right of the 0.00 0.000.00 Posterior Descending Artery (AcM R PDA)

As shown, Table 1 includes a fractional flow reserve (FFR) parameter, anestimated stenosis parameter, and an estimated ischemia parameter for aplurality of segments corresponding to major vessels in the heart. Insome embodiments, the matrix 122 includes a fractional flow reserve(FFR) parameter, an estimated stenosis parameter, and an estimatedischemia parameter for a standardized myocardial segment map having 17segments of the heart including the Left Main Artery (LMA), the ProximalLeft Circumflex Artery (Prox LCX), the Mid-Left Circumflex Artery (MidLCX), the Distal Left Circumflex Artery (Dist LCX), the Left PosteriorAtrioventricular (LPAV), the First Obtuse Marginal Branch (OM1), theSecond Obtuse Marginal Brach (OM2), the Third Obtuse Marginal Branch(OM3), the Proximal Left Anterior Descending Artery (Prox LAD), the MidLeft Anterior Descending Artery (Mid LAD), the Distal Left AnteriorDescending Artery (Dist LAD), the Left Anterior Descending FirstDiagonal Branch (LAD D1), the Left Anterior Descending Second DiagonalBranch (LAD D2), the Proximal Right Coronary Artery (Prox RCA), the MidRight Coronary Artery (Mid RCA), the Distal Right Coronary Artery (DistRCA), and the Acute Marginal Brach Right of the Posterior DescendingArtery (AcM R PDA). In Table 1, the parameters for myocardial ischemiaestimation, stenosis identification, and/or fractional flow reserveestimation are shown in a range of 0 to 1. Other scaling or ranges maybe used.

Example Nested Functions to Generate Fractional Flow Reserve (FFR)Estimation

Tables 2-5 show example non-linear functions to generate FFR estimationsfor several segments corresponding to major vessels in the heart. InTable 2, an example function to determine a FFR estimation for the leftmain artery (“FFR_LEFTMAIN”) is provided.

TABLE 2 FFR_LEFTMAIN = 0.128467341682411*noisevectorRz*atan2(Alpharatio, DensityV4)

As shown in Table 2, the FFR estimation for the left main artery isdetermined based on extracted metrics and variables such as aZ-component parameter associated with the noise subspace 706(“noisevectorRz”), a Alphahull ratio parameter (“Alpharatio”), and asignal density cloud volume 4 (“DensityV4”).

In Table 3, an example function to determine a FFR estimation for themid right coronary artery (“FFR_MIDRCA”) is provided.

TABLE 3 FFR_MIDRCA = 0.0212870065789474*noisevectorRy*Alpharatio*DensityV3

As shown in Table 3, the FFR estimation for the mid right coronaryartery is determined based on extracted metrics and variables such as aY-component parameter associated with the noise subspace 706(“noisevectorRy”), the Alphahull ratio parameter (“Alpharatio”), and asignal density cloud volume 3 (“DensityV3”).

In Table 4, an example function to determine a FFR estimation for themid left artery descending (“FFR_MIDLAD”) is provided.

TABLE 4 FFR_MIDLAD = atan2(AspectRatio3, residueLevelMean)

As shown in Table 4, the FFR estimation for the mid left arterydescending is determined based on extracted metrics and variables suchas a ratio of volume to surface area for cloud cluster 3(“AspectRatio3”) and a wavelet residue mean XYZ (“residueLevelMean”).

In Table 5, an example function to determine a FFR estimation for theproximal left circumflex artery (“FFR_PROXLCX”) is provided.

TABLE 5 FPR_PROXLCX = 0.408884581034257*atan2(residueLevelVolume+vectorcloud6, DensityV4)

As shown in Table 5, the FFR estimation for the proximal left circumflexartery is determined based on extracted metrics and variables such as awavelet residue volume XYZ (“residueLevelVolume”), vector cloud 6 volume(“vectorcloud6”), and a signal density cloud volume 4 (“DensityV4”).

Example Wavelet Cleaning Operator

Referring again to FIG. 7, a wavelet operator 714 (shown as “waveletscleaning” 714) can perform an operation on the wide-band gradient signaldata 112 (or a derived data therefrom). It should be understood to thoseskilled in the art that other intermediate phase linear processing maybe perform on the signal data 112 prior to operation by the waveletoperator 714. In some embodiments, the wavelet operator 714 comprises aBiorthogonal wavelet 3.3 transform. FIGS. 10A and 10B are diagrams of anexample wavelet transformation (i.e., Biorthogonal wavelet 3.3) used togenerate a multi-dimensional wavelet-cleansed dataset, in accordancewith an illustrative embodiment. FIG. 10A shows a decomposition scalingfunction cp. FIG. 10B shows a decomposition wavelet function w. FIG. 11is a diagram of an example output 1102 of the wavelet cleaningoperation. The output 1102 is show in conjunction with the input 1104 tothe wavelet cleaning operation. The output, in some embodiments, is atime series dataset.

Referring still to FIG. 7, the output of the wavelet operator 714 iscombined and transformed, via phase space transformation 718, to producethe multi-dimensional wavelet-cleansed dataset 716. Feature topologyanalysis (also shown in block 718) is performed on the multi-dimensionalwavelet-cleansed dataset 716 to extract metrics and variables 712 a. Theextracted metrics and variables 712 a, in some embodiments, includemorphological, topologic, or functional features of themulti-dimensional wavelet-cleansed dataset including, for example, 3Dvolume value, a void volume value, a surface area value, a principalcurvature direction value, and a Betti number value. In someembodiments, the multi-dimensional wavelet-cleansed dataset may besegmented, or partitioned, into sub-regions to which metrics andvariables of these sub-regions are extracted. In some embodiments, avoid volume value, a surface area value, a principal curvature directionvalue, and a Betti number value is also determined for each sub-region.In some embodiments, the number of generated sub-regions (also referredto as number of segment) is between about 2 and about 20 (e.g., 2, 3, 4,5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20). In someembodiments, the number of sub-regions is greater than 20.

FIG. 8 is a diagram of a method 800 of performing feature topologyanalysis of the multi-dimensional wavelet-cleansed dataset. In someembodiments, the method 800 may be similarly performed on otherdatasets, such as the multi-dimensional noise subspace dataset 712 b andmulti-dimensional wavelet-cleansed dataset 712 c generated by each ofthe phase space analyses (e.g., residue subspace analysis and noisesubspace analysis) as described in relation to FIG. 7. As shown in FIG.8, a morphological, topologic, or functional feature extraction analysis(shown as “Topology Analysis” 802) includes, in some embodiments,computing 3D volumes, voids, and surface area for at least one cycle ofthe multi-dimensional wavelet-cleansed dataset as a space-time domaindataset using an alpha-hull operator 804. In some embodiments, thealpha-hull operator uses a static alpha radius. Further detail of thealpha-hull operator is described in Edelsbrunner et al.,“Three-dimensional alpha shapes,” ACM Transactions on Graphics, Vol. 13(1): 43-72 (1994), which is incorporated by reference herein in itsentirety. Other topologic or geometric encapsulation operations may beused, including, for example, but not limited to Delauney triangulation.Delaunay triangulations are triangulations on a set of points such thatno point is within the circumcircle of any triangle in thetriangulation, and the minimum angle of all the angles in each trianglein the triangulation is maximized.

Referring still to FIG. 8, the generated multi-dimensional output of thealpha-hull operator 806 may be further extracted to compute (operator808) principal direction, curvature direction, Betti numbers, and Bettivalues. In addition, the dataset as a space-time domain dataset isfurther segmented (via operator 810) into sub-regions and volume,surface area and aspect ratios are computed for these sub-regions alsousing an alphahull operator 812. As shown, the space-time domain datasetis segmented into 5 regions, 8 regions, and 12 regions to which volume,surface area and aspect ratio parameters are computed for some of all ofthese regions. In some embodiments, the three group of regionscomprising 25 regions may generate 3 parameters for each regions toprovide 75 metrics or variables 712 a. In combination with the computedvolume, surface area, and aspect ratios of the alphahull output and theprincipal direction, curvature direction, Betti numbers, and Bettivalues thereof, there may be 82 metrics or variables 712 a. The metricsand variables 712 a may be provided as a matrix (shown as a “topologymatrix” 814).

It should be appreciated that other topologic features may be extractedin addition, or in substitute, those discussed herein. These featuresmay include properties such as energy, surface variations, etc., orgeometric features such as size.

It should be appreciated that other metrics and variables may beextracted and used depending on the number of operations performed andthat the example provided herein is merely for illustrative purposes.

Example Residue Subspace Analysis and Topology Extraction

Referring again to FIG. 7, attention is directed to a second phase spaceanalysis performed to determine metrics and variables 712 b for amulti-dimensional residue subspace dataset 704.

FIG. 12 is a diagram of an example wavelet-based operation 1202 togenerate the multi-dimensional residue subspace dataset 704 as describedin relation to FIG. 7, in accordance with an illustrative embodiment. Asshown in both FIGS. 7 and 12, multi-dimensional residue subspace dataset704 is generated as a residue (e.g., a subtraction operator 1202 in FIG.12) of two wavelet operators (e.g., 714 and 720). The first waveletoperator may be the wavelets cleaning 714, for example, using thebiorthogonal wavelet 3.3 operator. The second wavelet operator may be aReverse Biorthogonal Wavelet 3.7 operator 720.

FIGS. 13A and 13B are diagrams of an example wavelet transformation(i.e., Reverse Biorthogonal wavelet 3.7) used to generate amulti-dimensional residue subspace dataset, in accordance with anillustrative embodiment. FIG. 13A shows a decomposition scaling functionφ. FIG. 13B shows a decomposition scaling function ψ. It should be thatother phase linear wavelet operators may be used.

Referring still to FIG. 7, each residue output of the wavelet operator714 and wavelet operator 720 for each of the gradient signals arecombined and transformed, via phase space transformation, to produce themulti-dimensional residue subspace dataset 704. Feature topologyanalysis (also shown in block 722) is performed on the multi-dimensionalwavelet residue dataset to extract metrics and variables 712 b. Theextracted metrics and variables 712 b may include morphological,topologic, or functional features of the multi-dimensional waveletresidue dataset including, for example, 3D volume value, a void volumevalue, a surface area value, a principal curvature direction value, anda Betti number value. In some embodiments, the multi-dimensional waveletcleansed dataset may be segmented, or partitioned, into sub-regions towhich metrics and variables of these sub-regions are extracted. In someembodiments, a void volume value, a surface area value, a principalcurvature direction value, and a Betti number value is also determinedfor each sub-region. In some embodiments, the number of generatedsub-regions (also referred to as number of segment) is between 2 andabout 20 (e.g., 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,18, 19, and 20). In some embodiments, the number of sub-regions isgreater than 20. In some embodiments, a similar or same topologyextraction analysis as described in relation to FIG. 8 may be performed.

FIG. 14 is a depiction of an example residue subspace 704 which resultsfrom subtracting wavelet models (e.g., 714 and 720) using biorthogonal3.3 and reverse biorthogonal 3.7 operations. The residue subspacerepresents parts of the biological signal that are effectively toocomplex and non-linear to fit (i.e., represented) with a single waveletfunction. This residue subspace is processed, transformed intorepresentative features, and used to study the dynamical and geometricalproperties of the cardiac gradient data.

FIG. 16 is a depiction of an example dynamical phase space volume objectthat has been colored by the residue subspace. The phase space volumeobject is generated by overlaying the value of the residue subspace as acolor intensity mapping upon the input wide-band gradient signal data.The lack of intensive coloring is indicative of the absence of ischemicmyocardial tissue. That is, FIG. 16 is an example dynamical phase spacevolume object of a healthy person.

FIG. 17 is a depiction of an example dynamical phase space volume objectassociated with an ischemic patient. That is, the dynamical phase spacevolume object was generated using wide-band gradient signal data of apatient diagnosed with an ischemic myocardium. The dynamical phase spacevolume object has been colored by the residue subspace by overlaying thevalue of the residue subspace as a color intensity mapping upon theinput wide-band gradient signal data. The intensive coloring(corresponding to arrow 1702) is indicative of the presence of anischemic myocardium.

Example Noise Subspace Analysis and Topology Extraction

Referring again to FIG. 7, attention is directed to a third phase spaceanalysis performed to determine metrics and variables 712 c for amulti-dimensional noise subspace dataset 706. As shown in FIG. 7, themulti-dimensional noise subspace dataset 706 may be computed bysubtracting, via a subtraction operator 724, the input wide-bandgradient signal data 112 (or a dataset derived therefrom) and the outputof the wavelet cleansed signal data 716. The outputs of the subtractionoperation are combined and transformed, via phase space transformation,to produce the multi-dimensional residue subspace dataset 706. Featuretopology analysis (also shown in block 726) is performed on themulti-dimensional noise subspace dataset to extract metrics andvariables 712 c. The extracted metrics and variables 712 c may includemorphological, topologic, or functional features of themulti-dimensional wavelet residue dataset including, for example, 3Dvolume value, a void volume value, a surface area value, a principalcurvature direction value, and a Betti number value. In someembodiments, the multi-dimensional wavelet cleansed dataset may besegmented, or partitioned, into sub-regions to which metrics andvariables of these sub-regions are extracted. In some embodiments, avoid volume value, a surface area value, a principal curvature directionvalue, and a Betti number value is also determined for each sub-region.In some embodiments, the number of generated sub-regions (also referredto as number of segments) is between 2 and about 20 (e.g., 2, 3, 4, 5,6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20). In someembodiments, the number of sub-regions is greater than 20. In someembodiments, a similar or same topology extraction analysis as describedin relation to FIG. 8 may be performed.

FIG. 15 is a depiction of the noise subspace 706, which is the result ofsubtracting a biorthogonal 3.3 wavelet model (e.g., 714) from the inputwide-band gradient data 112. Similar to the residue subspace 704, itcontains complex dynamical information. Specifically, the noise subspacecontains chaotic information that cannot be effectively captured in amodel. This noise subspace is processed, transformed into representativefeatures, and used to study the dynamical and geometrical properties ofthe cardiac gradient data.

FIG. 18 is a depiction of an example noise subspace phase space objectthat has been colored by the noise subspace. The phase space object isgenerated by overlaying the value of the noise subspace as a colorintensity mapping upon a derivative transformation (e.g., a numericfractional derivative) of the input wide-band gradient signal data (or aderived data thereof). As shown in FIG. 18, the lack of intensivecoloring is indicative of the absence of an ischemic myocardium. Thatis, FIG. 18 is an example noise subspace phase space object of a healthyperson.

FIG. 19 is a depiction of an example noise subspace phase space objectassociated with an ischemic patient. The phase space object has beencolored by the noise subspace by overlaying the value of the noisesubspace as a color intensity mapping upon a derivative transformation(e.g., a numeric fractional derivative) of the input wide-band gradientsignal data (or a derived data thereof). The intensive coloring(corresponding to arrow 1902) is indicative of the presence of anischemic myocardium.

Example Machine Learning Analysis

FIG. 9 is a diagram of a method of performing machine learning analysisto create and select non-linear models to identify and/or estimate adegree of myocardial ischemia, identify one or more stenoses, and/orlocalize and/or estimate fractional flow reserve, as described inrelation to FIG. 8, in accordance with an illustrative embodiment. Asshown in FIG. 9, angiographic dataset 902 and fractional flow dataset904 are used to create (via operation 906) candidate non-linear modelsto identify stenosis (and/or estimate a degree thereof) and estimatefractional flow reserve 914. Examples of the generation of non-linearmodels, e.g., to estimate cardiac chamber size and mechanical function,are described, for example, in U.S. application Ser. No. 14/295,615,titled “Noninvasive electrocardiographic method for estimating mammaliancardiac chamber size and mechanical function”, which is incorporated byreference herein in its entirety.

In some embodiments, machine learning algorithms 908 are then used toselect a family of non-linear models 910 from the candidate non-linearmodels using wide-band gradient cardiac signal data 912 of patients orsubjects with some degree of stenosis and ischemia. In some embodiments,the machine learning algorithms are based on Regression Random Forestalgorithms or a modified variation thereof. In some embodiments, themachine learning algorithms are based on deep learning algorithms.

In some embodiments, the machine learning phase invokes a meta-geneticalgorithm to automatically select a subset of features drawn from alarge pool. This feature subset is then used by an AdaBoost algorithm togenerate predictors to diagnose significant coronary artery diseaseacross a population of patients representing both positive and negativecases. The performances of the candidate predictors are determinedthrough verification against a previously unseen pool of patients.Further description of the AdaBoost algorithm is provided in Freund,Yoav, and Robert E. Schapire, “A decision-theoretic generalization ofon-line learning and an application to boosting,” European conference oncomputational learning theory. Springer, Berlin, Heidelberg (1995),which is incorporated by reference herein in its entirety.

In some embodiments, space-time quantities can mapped to complex PhaseSpace differences in 12-dimensional space. Spatial changes in the phasespace matrix can be extracted using a non-Fourier integral which createsthe 12-dimensional space-time density metrics. These metrics for theventricle are modeled using a genetic algorithm to link 17 nonlinearnested sinusoidal Gaussian equations, for the ventricles 17 Segments ofthe Coronary Arterial Territories, as perfusion blockages. Perfusionimages were visually scored using a 17-segment model of the leftventricle and a 5-point scale (0=normal tracer uptake, 1=mildly reduced,2=moderately reduced, 3=severely reduced, 4=no uptake). The amount ofischemic myocardial tissue (IM) was calculated as the summed differencescore (the difference between summed stress and summed rest scores)divided by 80. Patients were classified as: no ischemia or equivocal(IM<5%), mild ischemia (5%≤IM<10%) and moderate/severe ischemia(IM≥10%). The output of these equations provides the amount and locationof the ischemic myocardial tissue.

In some embodiments, the wide-band biopotential data 112 are operatedupon with a modified matching pursuit (MMP) algorithm to create a sparsemathematical model. Detail of the MMP algorithm is provided in Mallat etal., “Matching Pursuits with Time-Frequency Dictionaries,” IEEETransactions on Signal Processing, Vol. 41 (12), Pages 3397-2415 (1993),the entirety of which is hereby incorporated by reference.

Characteristics of the model, including residue quantification, can beincluded in the feature set. The characteristics of the model may beextracted, in a feature extraction operation 706 (FIG. 7), to determinegeometric and dynamic properties of the model. These subspaces mayinclude, but are not limited to complex sub harmonic frequency (CSF)trajectory, quasi-periodic and chaotic subspaces, low/high energysubspaces, and fractional derivatives of the low/high energy subspaces.These subspaces are exemplars of the family of subspaces thatcharacterize the dynamics of the system, whether pathological or normal.

FIG. 20 is a diagram of a method of visualizing the estimated arterialflow characteristics in the heart, in accordance with an illustrativeembodiment. As shown in FIG. 20, a visualization engine 2002 receivesthe determined arterial flow characteristics and renders thecharacteristics onto a 3D visualization output. In some embodiments, thevisualization engine 2002 provides, in a graphical user interface (GUI),a system-level view of all of the arterial flow characteristics andtheir interactions. In some embodiments, the GUI presents the cascadingeffects of upstream modifications to the arterial flow upon thedownstream circulation.

Experimental Data

A coronary artery disease learning and formula development studyconducted under a clinical protocol collects resting phase signals fromhuman subjects prior to coronary angiography. The collected signals wereevaluated using the non-invasive acquisition and analysis methodsdescribed herein to detect the presence of significant coronary arterydisease in symptomatic adult patients or subjects. In addition, thecollected signals were evaluated to assess the left ventricular ejectionfraction and to identify the location of significant coronary arterydisease. The performance of the non-invasive acquisition and analysismethods described herein were evaluated using a comparative paired trialdesign; the results are shown in FIGS. 21 and 22.

Further description of this clinical protocol is provided in U.S.Provisional Appl. No. 62/340,410, titled “Method and System forCollecting Phase Signals for Phase Space Tomography Analysis,” which isincorporated by reference herein in its entirety.

FIGS. 21 and 22 are diagrams showing results of this study, which wasconducted on 523 human subjects, in accordance with an illustrativeembodiment. The presented data involves a prospective, non-randomizedtrial to refine the non-invasive acquisition and analysis methodsdescribed herein to detect and assess significant coronary arterydisease (CAD) using paired phase signals with clinical outcomes data asassessed during a catheterization procedure (i.e., either a ≥70%stenosis or a reduced fractional flow rate of <0.80).

In the presented data, data sets (total of 523) of 429 subjects are usedas the training data set, and data sets of 94 subjects are used as theverification population to assess sensitivity and specificity ofnon-invasive acquisition and analysis methods described herein. For acandidate predictor A (FIG. 21), the study provides a ROC curve of 0.80with a positive predictor value (PPV) of 47% and a negative predictorvalue (NPV) of 96% as compared to angiography results. For a candidatepredictor B (FIG. 22), the study provides a ROC curve of 0.78 with apositive predictor value (PPV) of 49% and a negative predictor value(NPV) of 92% as compared to angiography results. Candidate predictors Aand B are internal parameters (such as training classifiers) used in themachine training process.

As compared with diagnostic performance of non-invasive myocardialperfusion imaging using single-photon emission computed tomography,cardiac magnetic resonance, and positron emission tomography for thedetection of obstructive coronary artery disease as published in J. Am.Coll. Cardiol. 8:59(19), 1719-28 (May 2012) (shown as “SPECT”), thenon-invasive acquisition and analysis methods described herein (shown as“cPSTA”) performs comparably well. These solutions regularly achievedAUC-ROC scores greater than 0.7 in the verification phase, performing aswell or better than previous human-guided methods. Table 6 below showsdiagnostic performance between that study and the study herein.

TABLE 6 # of Sensitivity Specificity Diagnostic Test studies (95% CI)(95% CI) Odds Ratio SPECT 105 88% (88-89) 61% (59-62) 15.31 (13-19)cPSTA 1 92% (74-100) 62% (51-74) 19 (0-60) (predictor A) cPSTA 1 84%(64-95) 68% (57-79) 11.2 (0-41) (predictor B)

Having thus described several embodiments of the present disclosure, itwill be rather apparent to those skilled in the art that the foregoingdetailed disclosure is intended to be presented by way of example only,and is not limiting. Many advantages for non-invasive method and systemfor location of an abnormality in a heart have been discussed herein.Various alterations, improvements, and modifications will occur and areintended to those skilled in the art, though not expressly statedherein. These alterations, improvements, and modifications are intendedto be suggested hereby, and are within the spirit and the scope of thepresent disclosure. Additionally, the recited order of the processingelements or sequences, or the use of numbers, letters, or otherdesignations therefore, is not intended to limit the claimed processesto any order except as may be specified in the claims. Accordingly, thepresent disclosure is limited only by the following claims andequivalents thereto.

For example, further examples of phase space processing that may be usedwith the exemplified method and system are described in U.S. ProvisionalPatent Application No. 62/184,796, title “Latent teratogen-induced heartdeficits are unmasked postnatally with mathematical analysis and machinelearning on ECG signals”; U.S. patent application Ser. No. 15/192,639,title “Methods and Systems Using Mathematical Analysis and MachineLearning to Diagnose Disease”; U.S. patent application Ser. No.14/620,388, published as US2015/0216426, title “Method and system forcharacterizing cardiovascular systems from single channel data”; U.S.patent application Ser. No. 14/596,541, issued as U.S. Pat. No.9,597,021, title “Noninvasive method for estimating glucose,glycosylated hemoglobin and other blood constituents”; U.S. patentapplication Ser. No. 14/077,993, published as US2015/0133803, title“Noninvasive electrocardiographic method for estimating mammaliancardiac chamber size and mechanical function”; U.S. patent applicationSer. No. 14/295,615, title “Noninvasive electrocardiographic method forestimating mammalian cardiac chamber size and mechanical function”; U.S.patent application Ser. No. 13/970,582, issued as U.S. Pat. No.9,408,543, title “Non-invasive method and system for characterizingcardiovascular systems and all-cause mortality and sudden cardiac deathrisk”; U.S. patent application Ser. No. 15/061,090, published asUS2016/0183822, title “Non-invasive method and system for characterizingcardiovascular systems”; U.S. patent application Ser. No. 13/970,580,issued as U.S. Pat. No. 9,289,150, title “Non-invasive method and systemfor characterizing cardiovascular systems”; U.S. Patent Application No.62/354,668, titled “Method and System for Phase Space Analysis toDetermine Arterial Flow Characteristics”; and U.S. Provisional PatentApplication No. 61/684,217, title “Non-invasive method and system forcharacterizing cardiovascular systems”, which are each incorporated byreference in its entirety.

While the methods and systems have been described in connection withpreferred embodiments and specific examples, it is not intended that thescope be limited to the particular embodiments set forth, as theembodiments herein are intended in all respects to be illustrativerather than restrictive.

For example, the exemplified methods and systems may be used generatestenosis and FFR outputs for use with interventional system configuredto use the FFR/stenosis outputs to determine and/or modify a number ofstents and their placement intra operation.

Unless otherwise expressly stated, it is in no way intended that anymethod set forth herein be construed as requiring that its steps beperformed in a specific order. Accordingly, where a method claim doesnot actually recite an order to be followed by its steps or it is nototherwise specifically stated in the claims or descriptions that thesteps are to be limited to a specific order, it is no way intended thatan order be inferred, in any respect. This holds for any possiblenon-express basis for interpretation, including: matters of logic withrespect to arrangement of steps or operational flow; plain meaningderived from grammatical organization or punctuation; the number or typeof embodiments described in the specification.

Throughout this application, various publications are referenced. Thedisclosures of these publications in their entireties are herebyincorporated by reference into this application in order to more fullydescribe the state of the art to which the methods and systems pertain.

It will be apparent to those skilled in the art that variousmodifications and variations.

What is claimed is:
 1. A method for non-invasively identifying and/ormeasuring or estimating a degree of myocardial ischemia, identifying oneor more stenoses, and/or localizing and/or estimating fractional flowreserve, the method comprising: obtaining a plurality of wide-bandgradient signals simultaneously from the subject via at least oneelectrode; and determining, via one or more processors, one or morecoronary physiological parameters of the subject selected from the groupconsisting of a fractional flow reserve estimation, a stenosis value,and a myocardial ischemia estimation, based on a residue subspacedataset and a noise subspace dataset derived from data associated withthe plurality of wide-band gradient signals.
 2. The method of claim 1,wherein the residue subspace dataset is determined by: generating afirst wavelet signal dataset by performing a first wavelet operation ondata derived from the plurality of wide-band gradient signals;generating a second wavelet signal dataset by performing a secondwavelet operation on the first wavelet signal data; and subtractingvalues of the first wavelet signal dataset from values of the secondwavelet signal dataset to generate the residue subspace dataset, whereinthe residue subspace dataset comprises a three-dimensional phase spacedataset in a space-time domain.
 3. The method of claim 2, furthercomprising: extracting a first set of morphologic features of thethree-dimensional phase space dataset, wherein the first set ofextracted morphologic features include parameters selected from thegroup consisting of a 3D volume value, a void volume value, a surfacearea value, a principal curvature direction value, and a Betti numbervalue.
 4. The method of any one of claims 1-3, wherein the first set ofextracted morphologic features is extracted using an alpha-hulloperator.
 5. The method of claim 3, further comprising: dividing thethree-dimensional phase space dataset into a plurality of segments eachcomprising non-overlapping portions of the three-dimensional phase spacedata set; and extracting a second set of morphologic features of each ofthe plurality of segments, wherein the second set of extractedmorphologic features includes parameters selected from the groupconsisting of a 3D volume value, a void volume value, a surface areavalue, a principal curvature direction value, and a Betti number value.6. The method of claim 5, wherein the second set of extractedmorphologic features is extracted using an alpha-hull operator.
 7. Themethod of claim 5, wherein the plurality of segments comprise a numberof segments selected from the group consisting of 3, 4, 5, 6, 7, 8, 9,10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and
 20. 8. The method of claim1, wherein the noise subspace dataset is determined by: generating afirst wavelet signal dataset by performing a first wavelet operation ondata derived from the plurality of wide-band gradient signals; andgenerating a second wavelet signal dataset by performing a secondwavelet operation on the first wavelet signal dataset, the secondwavelet signal dataset comprising the noise subspace dataset, whereinthe noise subspace dataset comprises a three-dimensional phase spacedataset in a space-time domain.
 9. The method of claim 8, furthercomprising: extracting a set of morphologic features of thethree-dimensional phase space dataset, wherein the set of extractedmorphologic features includes parameters selected from the groupconsisting of a 3D volume value, a void volume value, a surface areavalue, a principal curvature direction value, and a Betti number value.10. The method of claim 9, wherein the set of extracted morphologicfeatures is extracted using an alpha-hull operator.
 11. The method ofclaim 9, further comprising: dividing the three-dimensional phase spacedataset into a plurality of segments, each comprising non-overlappingportion of the three-dimensional phase space dataset; and extracting asecond set of morphologic features of each of the second plurality ofsegments, wherein the second set of extracted morphologic featuresinclude parameters selected from the group consisting of a 3D volumevalue, a void volume value, a surface area value, a principal curvaturedirection value, and a Betti number value.
 12. The method of claim 11,wherein the second set of extracted morphologic features is extractedusing an alpha-hull operator.
 13. The method of claim 11, wherein thesecond of segments comprises a number of segment selected from the groupconsisting of 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,19, and
 20. 14. The method of claim 1, wherein the residue subspacedataset is associated with a first shape of a first noise geometry, andwherein the noise subspace dataset is associated with a second shape ofa second noise geometry corresponding to noise.
 15. The method of claim1, wherein the plurality of wide-band gradient signals is simultaneouslyobtained having a lag or skew of less than about 10-femtoseconds betweeneach of the signals.
 16. The method of claim 1, wherein each of theplurality of wide-band gradient signals is unfiltered prior to, andduring, the processing, to generate the residue subspace dataset and thenoise subspace dataset.
 17. The method of claim 1, wherein each of theplurality of wide-band gradient signals comprises cardiac data in afrequency domain having frequency components greater than about 1 kHz.18. The method of claim 1, wherein each of the plurality of wide-bandgradient signals comprises cardiac frequency information at a frequencyselected from the group consisting of about 1 kHz, about 2 kHz, about 3kHz, about 4 kHz, about 5 kHz, about 6 kHz, about 7 kHz, about 8 kHz,about 9 kHz, and about 10 kHz.
 19. The method of claim 1, wherein eachof the plurality of wide-band gradient signals comprises cardiacfrequency information at a frequency between about 0 Hz and about 50kHz.
 20. The method of claim 1, wherein each of the plurality ofwide-band gradient signals comprises cardiac frequency information at afrequency between about 0 Hz and about 500 kHz.
 21. The method of claim1, further comprising: associating, via a first machine learningoperation, the extracted first set of morphologic features to aplurality of candidate models associated with estimation of thefractional flow reserve estimation, the stenosis value, and themyocardial ischemia estimation; and selecting a candidate model of theplurality of candidate models to determine an output of each of theestimation of the fractional flow reserve estimation, the stenosisvalue, and the myocardial ischemia estimation.
 22. The method of claim1, further comprising: visualizing the determined one or more coronaryphysiological parameters.
 23. The method of claim 21, wherein thefractional flow reserve estimation, the stenosis value, and themyocardial ischemia estimation are presented at one or morecorresponding coronary regions on an image of a heart.
 24. The method ofclaim 1, further comprising: outputting, to a surgical device or adiagnostic device, the determined one or more coronary physiologicalparameters.
 25. The method of claim 1, wherein one of more of the atleast one electrodes are selected from the group consisting of surfaceelectrodes, intracardiac electrodes, and non-contact electrodes.
 26. Themethod of claim 1, additionally comprising the step of identifying oneor more significant stenoses, the identification having an AUC-ROC scoregreater than 0.7 in a verification phase.
 27. A system fornon-invasively identifying and/or measuring or estimating a degree ofmyocardial ischemia, identifying one or more stenoses, and/or localizingand/or estimating fractional flow reserve, the system comprising: aprocessor; and a memory having instructions stored thereon, whereinexecution of the instructions causes the processor to: obtain aplurality of wide-band gradient signals simultaneously from at least oneelectrode; and determine one or more coronary physiological parametersselected from the group consisting of a fractional flow reserveestimation, a stenosis value, and a myocardial ischemia estimation,based on a residue subspace dataset and a noise subspace dataset derivedfrom data associated with the plurality of wide-band gradient signals.28. The system of claim 27, wherein execution of the instructionsfurther causes the processor to: cause visualization of the determinedcoronary physiological parameter to be presented on a display.
 29. Thesystem of claim 27, wherein execution of the instructions further causesthe processor to: output, to a therapy device, the determined one ormore coronary physiological parameters.
 30. A computer readable mediumhaving instructions stored thereon, wherein execution of theinstructions further causes a processor to: determine one or morecoronary physiological parameters selected from the group consisting ofa fractional flow reserve estimation, a stenosis value, and a myocardialischemia estimation, based on a residue subspace dataset and a noisesubspace dataset derived from data associated with the plurality ofwide-band gradient signals simultaneously obtained from at least onesurface electrode.
 31. The computer readable medium of 30, whereinfurther execution of the instructions causes the processor to: causevisualization of the determined coronary physiological parameter to bepresented on a display.
 32. The computer readable medium of claim 30,wherein execution of the instructions further causes the processor to:output, to a therapy device, the determined one or more coronaryphysiological parameters.